Strong solutions for stochastic differential equations with jumps

TL;DR

This paper establishes criteria for the existence and uniqueness of strong solutions to stochastic differential equations with jumps, especially those driven by spectrally positive Lévy processes, under non-Lipschitz conditions.

Contribution

It extends the Yamada-Watanabe criteria to stochastic equations with jumps, providing new conditions for strong solution existence and uniqueness.

Findings

Criteria for strong solution existence under non-Lipschitz conditions

Application to equations driven by spectrally positive Lévy processes

Extension of Yamada-Watanabe theory to jump processes

Abstract

General stochastic equations with jumps are studied. We provide criteria for the uniqueness and existence of strong solutions under non-Lipschitz conditions of Yamada-Watanabe type. The results are applied to stochastic equations driven by spectrally positive L\'evy processes.